实用数据结构整理

     实用数据结构

                   1 基础数据结构回顾

                            1.1 抽象数据类型（ADT）

                                     基础的栈、队列……

                            1.2 优先队列

                                     priority_queue;

                                     堆优化的队列（常数是make_heap的好几倍）

                            1.3 并查集

                                     int find(int x){

                                               return fa[x]==x?x:fa[x]=find(fa[x]);

                                     }

                                     时间复杂度：O(α(x))//α(x)<=4

                   2 区间信息的维护与查询

                            2.1 二叉索引树（树状数组）

                                     int lowbit(int &x){
                                            return x&-x;
                                    }
                                    void updata(int p,int v){
                                            for(int i=p;i<=n;i+=lowbit(i)) c[i]+=v;
                                    }
                                    int query(int p){
                                            int res=0;
                                            for(int i=p;i;i-=lowbit(i)) res+=c[i];
                                            return res;
                                    }
                                1)单点修改，区间求和：
                                        updata(x,y);//O(log2(n))
                                        printf("%d\n",query(y)-query(x-1));//O(log2(n))
                                2)区间修改，单点查询：
                                        updata(x,z);updata(y+1,-z);;//O(log2(n))
                                        printf("%d\n",query(x));//O(log2(n))

                            2.2 RMQ问题

                                     1)对于max/min问题：

                                               预处理：O(nlog2(n))//log2(n)<=20

                                               查询：O(1)

                                               修改：等价<=>预处理

                                     2)对于其他问题(如求和，etc)：

                                               建议不要用

                                                

                            2.3 线段树（1）：点修改

                                     建树：O(nlog2(n))

                                     单次修改：O(log2(n))

                                     单次查询：O(log2(n))

                                     空间支撑：4*n

                            2.4 线段树（2）：区间修改

                                     建树：O(nlog2(n))

                                     加上lazy-tage

                                     单次修改：<= O(log2(n))

                                     单次查询：<= O(log2(n))

                                     (数据量越大，lazy-tage优化越明显)

                                     空间支撑：4*n

                   3 字符串（1）

                            3.1 Trie

                                     预处理：O(maxlen*kinds)//maxlen为最大字符串长度，kinds为所有字符串中字符种类数目

                                     查询：O(logn)

                            3.2 KMP算法

                                     预处理：O(n):fail[]/next[]

                                     查询：O(n)匹配

                             3.3 Manacher算法

                                    O(n):p[i]往两边扩展,更新id,mx

                            3.4 Aho-Corasick自动机

                                     Trie的升级版，加了队列处理

                   //以下不会

                   4 字符串（2）

                            4.1 后缀数组

                            4.2 最长公共前缀（LCP）

                            4.3 基于哈希值的LCP算法

                   5 排序二叉树

                            5.1 基本概念

                            5.2 用Treap实现名次树

                            5.3 用伸展树实现可分裂与合并的序列